How should I design the jaw for rigify pitchipoy?
When rigging you need to be clear about what you want to achieve, because every little function takes time to accommodate for. Which also means that I cannot give you the perfect answer unless you describe your character more clearly. If you want a character with a normal organic jaw, then skip the following paragraph.

The only reason you would parent something without weight paints is if you want a ridged object attached. If this character had an iron jaw for example, it might make sense. I'm not sure if pitchipoy is built for that, but if you were to attach it to just one bone you could probably achieve a ridged effect. However, that would make some mesh items harder to track down. So i'd recommend a ridged bind (flood the influence to one bone) that is IF you want a ridged jaw. 

If you want a normal organic jaw, then ignore your tutorial and find a better one because organic meshes generally require weight binding. I'd follow the official video for that: https://www.youtube.com/watch?v=-dwCXMc2V0U

The only thing i'd advise making into separate geometry is the teeth and tongue. That's just so that it's easier and more clean of a job when weight painting. Teeth can have ridged weighting, tongue can have auto weights. For the mouth, it's just a concave section of geometry, and of course attached to the rest of the surround mesh. You will need to ensure that the weights do not collapse the geo into the teeth and tongue when the character open's it's mouth.